功能梯度材料弹塑性本构关系及其圆柱壳弹塑性屈曲理论研究

As important components of structural stability theory, elastic buckling issues of composite plates and shells have always been concerned. With the increasing engineering application of functionally graded materials(FGM), systematical researches have been witnessed on elastic buckling of FGM cylindrical shells usually suitable for thin ones. However, no relevant research or report was found on the topic of elastoplastic buckling of medium and thick FGM cylindrical shells. The bottleneck problems primly lied behind is the complicated constitutive model of ceramic/metallic FGM and the moving elastoplastic interface of the material which is difficult to be characterized and handled by theoretical method. By combining material experiment, theoretical analysis, and numerical simulation, this project would study on the elastoplastic buckling of FGM cylindrical shells. Although there is still some difficult, it would further improve the elastoplastic stability theory of plates and shells. In the research, uniaxial tensional experiments of ceramic/metallic even mixture will be carried out to obtain the elastoplastic parameters of FGM. The J2 deformation theory would help to found the material elastoplastic constitutive model of FGM. By employing the Mises yield criterion, the material elastoplastic interface is characterized theoretically with the aid of the prebuckling stress state and the elastoplastic material parameters. Finally, based on the shear deformation theory, a set of theoretical method for elastoplastic buckling issue of FGM cylindrical shells will be developed, and the elastoplastic buckling behaviors and plastic buckling behaviors will be investigated deeply.

作为结构稳定理论的重要组成部分，复合材料板壳弹塑性屈曲问题的研究向来备受关注。随着功能梯度材料工程应用的日益广泛，适用于其薄板壳的弹性屈曲理论已较为成熟，但却未见针对其中厚、厚板壳弹塑性屈曲问题的相关研究，瓶颈在于功能梯度材料复杂的材料本构关系及其运动的材料弹塑性交界面在理论上难以表征和处理。结合材料实验、理论分析、数值模拟的方法，本项目将开展功能梯度材料圆柱壳弹塑性屈曲问题的研究工作，项目本身具有一定难度，将进一步完善板壳弹塑性稳定理论。研究中对陶瓷/金属均匀共混材料进行单轴拉伸实验，得到功能梯度材料的弹塑性参数，并应用全量理论建立材料的弹塑性本构关系；进而采用Mises屈服准则，结合壳体的前屈曲应力状态以及材料的弹塑性参数，得到材料的弹塑性交界面的理论表征方法；最后基于剪切变形理论，发展一整套功能梯度材料圆柱壳弹塑性屈曲问题的理论分析方法，并对其弹塑性屈曲、塑性屈曲行为进行深入的研究。

作为结构稳定理论的重要组成部分，复合材料板壳弹塑性屈曲问题的研究向来备受关注。结合理论分析、数值模拟的方法，本项目研究了功能梯度材料（FGM）圆柱壳、椭圆柱壳、矩形板、圆环结构的弹塑性屈曲问题，完善了非匀质板壳的弹塑性稳定理论。通过将FGM的材料梯度特征引入传统的材料弹塑性理论，建立了FGM材料的弹塑性本构关系；进而采用Mises屈服准则和结构的前屈曲应力状态分析，在均匀应变的假设下，该项目不仅得到材料弹塑性交界面位置的理论解析方法，还发展了一种FGM板壳结构弹塑性屈曲问题的理论分析方法。理论结果通过数值模拟结果及实验结果验证，充分说明理论的合理性。最后，针对不同FGM结构开展弹塑性屈曲、塑性屈曲行为的分析，得到材料弹塑性参数、材料非均匀参数对结构屈曲的影响。